%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU454^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:07 AM UTC 2026
% Result : Theorem 0.24s 0.40s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 28 unt; 0 typ; 3 def)
% Number of atoms : 415 ( 130 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 253 ( 29 ~; 83 |; 0 &; 134 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 49 usr; 8 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 53 ( 0 sgn 1 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
sK0: $i > $i > $o ).
thf(f3,axiom,
( idem
= ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] :
( ( X0 @ ( X0 @ X1 ) )
= ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',idempotent) ).
thf(f8,axiom,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive_closure) ).
thf(f30,conjecture,
idem @ rc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive_closure_op_is_idempotent) ).
thf(f31,negated_conjecture,
~ ( idem @ rc ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f35,plain,
( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f44,plain,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f45,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f86,plain,
~ ( idem @ rc ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
( ( idem @ rc )
!= $true ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( ( idem @ rc )
!= $true ),
inference(flattening,[],[f87]) ).
thf(f91,plain,
( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f96,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f118,plain,
( ( idem @ rc )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f136,plain,
( $true
!= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(definition_unfolding,[],[f118,f91,f96]) ).
thf(f137,plain,
( $true
!= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= ( ^ [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= ( ^ [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( $false
= ( ( ^ [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) )
= ( ^ [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) )
!= ( ^ [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) ) ) ),
inference(equality_proxy_clausification,[],[f139]) ).
thf(f148,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) )
@ sK1 )
!= ( ^ [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ( Y0 = Y1 )
| ( sK0 @ Y0 @ Y1 ) )
@ sK1 ) ),
inference(negative_extensionality,[],[f140]) ).
thf(f149,plain,
( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 @ sK1 @ Y0 ) ) )
!= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK1 = Y0 )
| ( sK0 @ sK1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 @ sK1 @ Y0 ) )
@ sK2 )
!= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK1 = Y0 )
| ( sK0 @ sK1 @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f149]) ).
thf(f151,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 @ sK1 @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK1 = Y0 )
| ( sK0 @ sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 @ sK1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK1 = Y0 )
| ( sK0 @ sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f150]) ).
thf(f153,plain,
( ( $false
= ( ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) )
| ( $false
= ( ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( sK0 @ sK1 @ sK2 ) )
| ( $false
= ( ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( sK1 = sK2 ) )
| ( $false
= ( ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f156,plain,
( ( sK1 != sK2 )
| ( $false
= ( ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) ) ),
inference(equality_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( sK1 != sK2 )
| ( $false
= ( sK1 = sK2 ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f159,plain,
( ( sK1 != sK2 )
| ( sK1 != sK2 ) ),
inference(equality_proxy_clausification,[],[f158]) ).
thf(f160,plain,
sK1 != sK2,
inference(duplicate_literal_removal,[],[f159]) ).
thf(f165,plain,
( ( $false
= ( sK0 @ sK1 @ sK2 ) )
| ( $false
= ( ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f168,plain,
( ( $false
= ( sK0 @ sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f171,plain,
( $false
= ( sK0 @ sK1 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f168]) ).
thf(f172,plain,
( ( $true
= ( ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) )
| ( $true
= ( ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f173,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ( $true
= ( ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) )
| ( $true
= ( sK1 = sK2 ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ( $true
= ( ( sK1 = sK2 )
| ( sK0 @ sK1 @ sK2 ) ) )
| ( $true
= ( sK1 = sK2 ) )
| ( $true
= ( sK1 = sK2 ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ( $true
= ( sK1 = sK2 ) )
| ( $true
= ( sK1 = sK2 ) )
| ( $true
= ( sK1 = sK2 ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK1 = sK2 ) ),
inference(equality_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ( sK1 = sK2 ) ),
inference(duplicate_literal_removal,[],[f176]) ).
thf(f179,definition,
( spl3_1
<=> ( $false
= ( sK0 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f181,plain,
( ( $false
= ( sK0 @ sK1 @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f179]) ).
thf(f183,definition,
( spl3_2
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f189,plain,
spl3_1,
inference(avatar_split_clause,[],[f171,f179]) ).
thf(f191,definition,
( spl3_3
<=> ( $true
= ( sK0 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f193,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f194,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f177,f191,f183]) ).
thf(f195,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f160,f183]) ).
thf(f197,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(constrained_superposition,[],[f181,f193]) ).
thf(f201,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f202,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f201]) ).
cnf(s4,plain,
spl3_1,
inference(sat_conversion,[],[f189]) ).
cnf(s5,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f194]) ).
cnf(s6,plain,
~ spl3_2,
inference(sat_conversion,[],[f195]) ).
cnf(s9,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f202]) ).
cnf(s10,plain,
spl3_3,
inference(rat,[],[s5,s6]) ).
cnf(s11,plain,
~ spl3_1,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s4,s11]) ).
thf(f204,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU454^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.29 % Computer : n015.cluster.edu
% 0.24/0.29 % Model : x86_64 x86_64
% 0.24/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.29 % Memory : 8046.5625MB
% 0.24/0.29 % OS : Linux 6.8.0-71-generic
% 0.24/0.29 % CPULimit : 300
% 0.24/0.29 % WCLimit : 300
% 0.24/0.29 % DateTime : Tue Sep 29 13:44:49 UTC 2026
% 0.24/0.29 % CPUTime :
% 0.24/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.34 Running first-order model finding
% 0.24/0.34 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.40 % (3545330)Will run a generic schedule for satisfiability detection.
% 0.24/0.40 % (3545338)dis+10_1_sil=32000:sp=arity:random_seed=1424068777:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.40 % (3545338) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3545330-3545338"...
% 0.24/0.40 % (3545336)% WARNING: option uhcvi not known.
% 0.24/0.40 % (3545338)...printing done.
% 0.24/0.40 % (3545338)Refutation found. Thanks to Tanya!
% 0.24/0.40 % SZS status Theorem for theBenchmark
% 0.24/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.40 % (3545338)------------------------------
% 0.24/0.40 % (3545338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.40 % (3545338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.40 % (3545338)CaDiCaL version: 2.1.3
% 0.24/0.40 % (3545338)Termination reason: Refutation
% 0.24/0.40 % (3545338)Time elapsed: 0.007 s
% 0.24/0.40 % (3545338)Peak memory usage: 13 MB
% 0.24/0.40 % (3545338)Instructions burned: 13 (million)
% 0.24/0.40 % (3545330)Success in time 0.041 s
% 0.24/0.40 % Vampire exiting
%------------------------------------------------------------------------------